EU, Russia urge 'maximum restraint' for those 'locked and loaded' over Saudi Aramco attacks
A US response, Trump said, would be forthcoming if Saudi Arabia confirms who is behind the attacks claimed by Yemen's Iran-linked Houthi rebels.
The EU on Monday urged "maximum restraint" in response to the strikes on two key Saudi oil facilities.
Russia also called for countries involved to avoid taking "hasty steps" that would escalate the crisis.
Analysts had hoped that the exit of hardline anti-Iran National Security Advisor John Bolton - the architect of Washington's "maximum pressure" campaign on Tehran - would provide an opening for the easing of tensions in the Gulf.
But Saturday's attacks on the Abqaiq plant, the world's largest oil processing facility, and nearby Khurais, which hosts a massive oil field, have thrown a wrench in such aspirations.
"We seem [the attacks] as a real threat to regional security, and at a time that tensions in the region are running very high, this attack undermines ongoing work at de-escalation and dialogue," EU spokeswoman Maja Kocijancic said on Monday.
Kremlin spokesman Dmitry Peskov echoed those comments, calling on "all countries to avoid hasty steps or conclusions that could exacerbate the situation".
"This is a very unpleasant story," he said on Monday."We are hoping that Saudi Arabia will be able to cope with the inflicted damage in the nearest future."
The Houthi rebels on Monday threatened more attacks on Saudi Aramco's oil processing plants, warning that the state-own energy firm's operations could be targeted at "any moment".
The Yemeni rebel group has claimed previous drone attacks on Saudi oil infrastructure and airports over the past year.
The US, however, blamed attacks supposedly launched by the Houthis earlier this year on Iran-linked militants in Iraq.
Secretary of State Mike Pompeo has blamed Saturday's drone strikes on Iran, claiming that the attacks couldn't have been directed from Yemen.
A suspicious drone sighting over Kuwait on Saturday has raised the possibility that the attacks could have been directed from Iraq.
Baghdad has denied any links to the strikes.